Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

For a commutative ring $R$, I can consider $\operatorname{GL}_n(R)$ as a group scheme over $\operatorname{Spec} R$. Are there analogs of this notion when $R$ is non-commutative, say $R = \operatorname{End}_k V$ (for $V$ a finite-dimensional $k$-vector space), which retain any useful part of the theory of group schemes?

share|improve this question
    
Well, it's easy to define a group-valued functor on the category of not-necessarily-commutative rings. But group schemes in the usual sense are very special group-valued functors, and it is not so easy to generalise that part of the definition to the non-commutative setting. –  Zhen Lin Nov 3 '12 at 1:16
    
I know it's tough; that's why I asked. I was thinking in terms of modern notions of spec of a noncommutative ring (which I don't really understand). –  Daniel McLaury Nov 3 '12 at 4:16

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.